def test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches the finite difference jacobian
"""
coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5]
edgeSpecies = []
rxn1 = Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K')))
coreReactions = [rxn1]
edgeReactions = []
numCoreSpecies = len(coreSpecies)
rxnList = []
rxnList.append(Reaction(reactants=[self.C2H6], products=[self.CH3,self.CH3], kinetics=Arrhenius(A=(686.375*6,'1/s'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.CH3,self.CH3], products=[self.C2H6], kinetics=Arrhenius(A=(686.375*6,'m^3/(mol*s)'), n=4.40721, Ea=(7.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H6,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H5,self.CH4], products=[self.C2H6,self.CH3], kinetics=Arrhenius(A=(46.375*6,'m^3/(mol*s)'), n=3.40721, Ea=(6.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H5,self.CH4], products=[self.CH3,self.CH3,self.CH3], kinetics=Arrhenius(A=(246.375*6,'m^3/(mol*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.CH3,self.CH3,self.CH3], products=[self.C2H5,self.CH4], kinetics=Arrhenius(A=(246.375*6,'m^6/(mol^2*s)'), n=1.40721, Ea=(3.82799,'kcal/mol'), T0=(298.15,'K'))))#
rxnList.append(Reaction(reactants=[self.C2H6,self.CH3,self.CH3], products=[self.C2H5,self.C2H5,self.H2], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H5,self.C2H5,self.H2], products=[self.C2H6,self.CH3,self.CH3], kinetics=Arrhenius(A=(146.375*6,'m^6/(mol^2*s)'), n=2.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.C2H6,self.C2H6], products=[self.CH3,self.CH4,self.C2H5], kinetics=Arrhenius(A=(1246.375*6,'m^3/(mol*s)'), n=0.40721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
rxnList.append(Reaction(reactants=[self.CH3,self.CH4,self.C2H5], products=[self.C2H6,self.C2H6], kinetics=Arrhenius(A=(46.375*6,'m^6/(mol^2*s)'), n=0.10721, Ea=(8.82799,'kcal/mol'), T0=(298.15,'K'))))
for rxn in rxnList:
coreSpecies = [self.CH4,self.CH3,self.C2H6,self.C2H5,self.H2]
edgeSpecies = []
coreReactions = [rxn]
c0={self.CH4:0.2,self.CH3:0.1,self.C2H6:0.35,self.C2H5:0.15, self.H2:0.2}
rxnSystem0 = LiquidReactor(self.T, c0,termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
dN = .000001*sum(rxnSystem0.y)
dN_array = dN*numpy.eye(numCoreSpecies)
dydt = []
for i in xrange(numCoreSpecies):
rxnSystem0.y[i] += dN
dydt.append(rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0])
rxnSystem0.y[i] -= dN # reset y to original y0
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
jacobian[i,j] = (dydt[j][i]-dydt0[i])/dN
self.assertAlmostEqual(jacobian[i,j], solverJacobian[i,j], delta=abs(1e-4*jacobian[i,j]))
def test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches
the finite difference jacobian.
"""
core_species = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edge_species = []
num_core_species = len(core_species)
c0 = {
self.CH4: 0.2,
self.CH3: 0.1,
self.C2H6: 0.35,
self.C2H5: 0.15,
self.H2: 0.2
}
edge_reactions = []
rxn_list = [
Reaction(reactants=[self.C2H6],
products=[self.CH3, self.CH3],
kinetics=Arrhenius(A=(686.375 * 6, '1/s'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.CH3, self.CH3],
products=[self.C2H6],
kinetics=Arrhenius(A=(686.375 * 6, 'm^3/(mol*s)'),
n=4.40721,
Ea=(7.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H6, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'),
n=3.40721,
Ea=(6.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H5, self.CH4],
products=[self.C2H6, self.CH3],
kinetics=Arrhenius(A=(46.375 * 6, 'm^3/(mol*s)'),
n=3.40721,
Ea=(6.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H5, self.CH4],
products=[self.CH3, self.CH3, self.CH3],
kinetics=Arrhenius(A=(246.375 * 6, 'm^3/(mol*s)'),
n=1.40721,
Ea=(3.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.CH3, self.CH3, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(246.375 * 6, 'm^6/(mol^2*s)'),
n=1.40721,
Ea=(3.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H6, self.CH3, self.CH3],
products=[self.C2H5, self.C2H5, self.H2],
kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'),
n=2.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H5, self.C2H5, self.H2],
products=[self.C2H6, self.CH3, self.CH3],
kinetics=Arrhenius(A=(146.375 * 6, 'm^6/(mol^2*s)'),
n=2.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.C2H6, self.C2H6],
products=[self.CH3, self.CH4, self.C2H5],
kinetics=Arrhenius(A=(1246.375 * 6, 'm^3/(mol*s)'),
n=0.40721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
Reaction(reactants=[self.CH3, self.CH4, self.C2H5],
products=[self.C2H6, self.C2H6],
kinetics=Arrhenius(A=(46.375 * 6, 'm^6/(mol^2*s)'),
n=0.10721,
Ea=(8.82799, 'kcal/mol'),
T0=(298.15, 'K'))),
]
# Analytical Jacobian for reaction 6
def jacobian_rxn6(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
jaco = np.zeros((5, 5))
jaco[1, 1] = -4 * kf * c1 * c2
jaco[1, 2] = -2 * kf * c1 * c1
jaco[1, 3] = 4 * kr * c3 * c4
jaco[1, 4] = 2 * kr * c3 * c3
jaco[2, 1:] = 0.5 * jaco[1, 1:]
jaco[3, 1:] = -jaco[1, 1:]
jaco[4, 1:] = -0.5 * jaco[1, 1:]
return jaco
# Analytical Jacobian for reaction 7
def jacobian_rxn7(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
jaco = np.zeros((5, 5))
jaco[1, 1] = -4 * kr * c1 * c2
jaco[1, 2] = -2 * kr * c1 * c1
jaco[1, 3] = 4 * kf * c3 * c4
jaco[1, 4] = 2 * kf * c3 * c3
jaco[2, 1:] = 0.5 * jaco[1, 1:]
jaco[3, 1:] = -jaco[1, 1:]
jaco[4, 1:] = -0.5 * jaco[1, 1:]
return jaco
for rxn_num, rxn in enumerate(rxn_list):
core_reactions = [rxn]
rxn_system0 = LiquidReactor(self.T, c0, 1, termination=[])
rxn_system0.initialize_model(core_species, core_reactions,
edge_species, edge_reactions)
dydt0 = rxn_system0.residual(0.0, rxn_system0.y,
np.zeros(rxn_system0.y.shape))[0]
dN = .000001 * sum(rxn_system0.y)
# Let the solver compute the jacobian
solver_jacobian = rxn_system0.jacobian(0.0, rxn_system0.y, dydt0,
0.0)
if rxn_num not in (6, 7):
dydt = []
for i in range(num_core_species):
rxn_system0.y[i] += dN
dydt.append(
rxn_system0.residual(0.0, rxn_system0.y,
np.zeros(rxn_system0.y.shape))[0])
rxn_system0.y[i] -= dN # reset y
# Compute the jacobian using finite differences
jacobian = np.zeros((num_core_species, num_core_species))
for i in range(num_core_species):
for j in range(num_core_species):
jacobian[i, j] = (dydt[j][i] - dydt0[i]) / dN
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 *
jacobian[i, j]))
# The forward finite difference is very unstable for reactions
# 6 and 7. Use Jacobians calculated by hand instead.
elif rxn_num == 6:
kforward = rxn.get_rate_coefficient(self.T)
kreverse = kforward / rxn.get_equilibrium_constant(self.T)
jacobian = jacobian_rxn6(c0, kforward, kreverse, core_species)
for i in range(num_core_species):
for j in range(num_core_species):
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 *
jacobian[i, j]))
elif rxn_num == 7:
kforward = rxn.get_rate_coefficient(self.T)
kreverse = kforward / rxn.get_equilibrium_constant(self.T)
jacobian = jacobian_rxn7(c0, kforward, kreverse, core_species)
for i in range(num_core_species):
for j in range(num_core_species):
self.assertAlmostEqual(jacobian[i, j],
solver_jacobian[i, j],
delta=abs(1e-4 *
jacobian[i, j]))
def test_jacobian(self):
"""
Unit test for the jacobian function:
Solve a reaction system and check if the analytical jacobian matches
the finite difference jacobian.
"""
coreSpecies = [self.CH4, self.CH3, self.C2H6, self.C2H5, self.H2]
edgeSpecies = []
numCoreSpecies = len(coreSpecies)
c0 = {self.CH4: 0.2, self.CH3: 0.1, self.C2H6: 0.35, self.C2H5: 0.15, self.H2: 0.2}
edgeReactions = []
rxnList = []
rxnList.append(Reaction(
reactants=[self.C2H6],
products=[self.CH3, self.CH3],
kinetics=Arrhenius(A=(686.375*6, '1/s'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.CH3, self.CH3],
products=[self.C2H6],
kinetics=Arrhenius(A=(686.375*6, 'm^3/(mol*s)'), n=4.40721, Ea=(7.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H6, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(46.375*6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H5, self.CH4],
products=[self.C2H6, self.CH3],
kinetics=Arrhenius(A=(46.375*6, 'm^3/(mol*s)'), n=3.40721, Ea=(6.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H5, self.CH4],
products=[self.CH3, self.CH3, self.CH3],
kinetics=Arrhenius(A=(246.375*6, 'm^3/(mol*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.CH3, self.CH3, self.CH3],
products=[self.C2H5, self.CH4],
kinetics=Arrhenius(A=(246.375*6, 'm^6/(mol^2*s)'), n=1.40721, Ea=(3.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H6, self.CH3, self.CH3],
products=[self.C2H5, self.C2H5, self.H2],
kinetics=Arrhenius(A=(146.375*6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H5, self.C2H5, self.H2],
products=[self.C2H6, self.CH3, self.CH3],
kinetics=Arrhenius(A=(146.375*6, 'm^6/(mol^2*s)'), n=2.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.C2H6, self.C2H6],
products=[self.CH3, self.CH4, self.C2H5],
kinetics=Arrhenius(A=(1246.375*6, 'm^3/(mol*s)'), n=0.40721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
rxnList.append(Reaction(
reactants=[self.CH3, self.CH4, self.C2H5],
products=[self.C2H6, self.C2H6],
kinetics=Arrhenius(A=(46.375*6, 'm^6/(mol^2*s)'), n=0.10721, Ea=(8.82799, 'kcal/mol'), T0=(298.15, 'K'))
))
# Analytical Jacobian for reaction 6
def jacobian_rxn6(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kf * c1 * c2
J[1, 2] = -2 * kf * c1 * c1
J[1, 3] = 4 * kr * c3 * c4
J[1, 4] = 2 * kr * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
# Analytical Jacobian for reaction 7
def jacobian_rxn7(c, kf, kr, s):
c1, c2, c3, c4 = c[s[1]], c[s[2]], c[s[3]], c[s[4]]
J = numpy.zeros((5, 5))
J[1, 1] = -4 * kr * c1 * c2
J[1, 2] = -2 * kr * c1 * c1
J[1, 3] = 4 * kf * c3 * c4
J[1, 4] = 2 * kf * c3 * c3
J[2, 1:] = 0.5 * J[1, 1:]
J[3, 1:] = -J[1, 1:]
J[4, 1:] = -0.5 * J[1, 1:]
return J
for rxn_num, rxn in enumerate(rxnList):
coreReactions = [rxn]
rxnSystem0 = LiquidReactor(self.T, c0, 1, termination=[])
rxnSystem0.initializeModel(coreSpecies, coreReactions, edgeSpecies, edgeReactions)
dydt0 = rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0]
dN = .000001*sum(rxnSystem0.y)
# Let the solver compute the jacobian
solverJacobian = rxnSystem0.jacobian(0.0, rxnSystem0.y, dydt0, 0.0)
if rxn_num not in (6, 7):
dydt = []
for i in xrange(numCoreSpecies):
rxnSystem0.y[i] += dN
dydt.append(rxnSystem0.residual(0.0, rxnSystem0.y, numpy.zeros(rxnSystem0.y.shape))[0])
rxnSystem0.y[i] -= dN # reset y
# Compute the jacobian using finite differences
jacobian = numpy.zeros((numCoreSpecies, numCoreSpecies))
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
jacobian[i, j] = (dydt[j][i]-dydt0[i])/dN
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
# The forward finite difference is very unstable for reactions
# 6 and 7. Use Jacobians calculated by hand instead.
elif rxn_num == 6:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn6(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
elif rxn_num == 7:
kforward = rxn.getRateCoefficient(self.T)
kreverse = kforward / rxn.getEquilibriumConstant(self.T)
jacobian = jacobian_rxn7(c0, kforward, kreverse, coreSpecies)
for i in xrange(numCoreSpecies):
for j in xrange(numCoreSpecies):
self.assertAlmostEqual(jacobian[i, j], solverJacobian[i, j], delta=abs(1e-4*jacobian[i, j]))
